COVID-19 and excess mortality in Russia: Regional estimates of life expectancy losses in 2020 and excess deaths in 2021.

Accurately counting the human cost of the COVID-19 at both the national and regional level is a policy priority. The Russian Federation currently reports one of the higher COVID-19 mortality rates in the world; but estimates of mortality differ significantly. Using a statistical method accounting for changes in the population age structure, we present the first national and regional estimates of excess mortality for 2021; calculations of excess mortality by age, gender, and urban/rural status for 2020; and mean remaining years of life expectancy lost at the regional level. We estimate that there were 351,158 excess deaths in 2020 and 678,022 in 2021 in the Russian Federation; and, in 2020, around 2.0 years of life expectancy lost. While the Russian Federation exhibits very high levels of excess mortality compared to other countries, there is a wide degree of regional variation: in 2021, excess deaths expressed as a percentage of expected deaths at the regional level range from 27% to 52%. Life expectancy loss is generally greater for males; while excess mortality is greater in urban areas. For Russia as whole, an average person who died due to the pandemic in 2020 would have otherwise lived for a further 14 more years (and as high as 18 years in some regions), disproving the widely held view that excess mortality during the pandemic period was concentrated among those with few years of life remaining-especially for females. At a regional level, less densely populated, more remote regions, rural regions appear to have fared better regarding excess mortality and life expectancy loss-however, a part of this differential could be owing to measurement issues. The calculations demonstrate more clearly the true degree of the human cost of the pandemic in the Russian Federation.

The inverse relationship between life expectancy-induced changes in the old-age dependency ratio and the prospective old-age dependency ratio.

Unlike other biological populations, the human population is experiencing long-run increases in life expectancy. Those lead to changes in age compositions not typical for other biological populations. Sanderson and Scherbov (2015a) demonstrated that, in many countries in Europe, faster increases in life expectancy lead to faster population aging when measured using the old-age dependency ratio and to slower population aging when measured using the prospective old-age dependency ratio that employs a dynamic old-age threshold. We examine this finding analytically and with simulations. We use an analytic decomposition of changes in mortality schedules into shift and compression processes. We show that shifts and compressions of mortality schedules push the two old-age dependency ratios in opposite directions. Our formal results are supported by simulations that show a positive effect of a mortality shift on the old-age dependency ratio and a negative effect of it on the prospective old-age dependency ratio. The effects are of opposite sign for a mortality compression. Our formal and simulation results generalize observed European trends and suggest that the inverse relationship between life expectancy and prospective old-age dependency would be observed more generally.

Constrained Mortality Extrapolation to Old Age: An Empirical Assessment.

This paper aims to improve the accuracy of parametric extrapolations of the death rates into old age by constraining the extrapolation model on presumed life expectancy at old age. Such a task is particularly important in cases where the data quality at old age, in particular the age exaggeration, is not sufficient for reliable mortality estimates. Our tests are based on period data from the Human Mortality Database and the use of the Horiuchi-Coale and Mitra formulas for reducing the bias of life expectancy in the open age interval. We show that extrapolation accuracy is substantially improved when the extrapolation is constrained by either the empirical life expectancy or the Horiuchi-Coale or Mitra estimates. Unconstrained extrapolations and those constrained by conventional life table estimates of life expectancy in the open age interval show substantial biases and should be avoided. Combining extrapolation with life expectancy estimates which are robust to the effects of age exaggeration appears to be a valuable way of improving mortality estimation.

Expectation of life at old age: revisiting Horiuchi-Coale and reconciling with Mitra.

Data quality issues at advanced old age, such as incompleteness of registration of vital events and age misreporting, compromise estimates of the death rates and remaining life expectancy at those ages. Following up on Horiuchi and Coale (Population Studies 36: 317-326, 1982), Mitra (Population Studies 38: 313-319, 1984, Population Studies 39: 511-512, 1985), and Coale (Population Studies 39: 507-509, 1985), we examine the conventional approaches to constructing life tables from data deficient at advanced ages and the two adjustment methods by the mentioned authors. Contrary to earlier reports by Horiuchi, Coale, and Mitra, we show that the two methods are consistent and useful in drastically reducing the estimation errors in life expectancy as compared to the conventional approaches, i.e., the classical open age interval model and extrapolation of the death rates. Our results suggest complementing the classical estimates of life expectancy by adjustments using Horiuchi-Coale, Mitra, or other appropriate methods and avoiding the extrapolation method as a tool for estimating the life expectancy.

Why increasing longevity may favour a PAYG pension system over a funded system.

When pension systems are contrasted it is common to use simplified demographic models, such as overlapping generation models with time-invariant mortality. Breaking with this tradition, we show that for a population with increasing longevity, the pay-as-you-go (PAYG) system may be more advantageous than a funded system (FS). Increasing longevity favours the PAYG system because for the workers living longer at retirement than current retirees, it is less costly to fund others' current pensions than their own. At present, the effect amounts to around 15 per cent in terms of the dependency ratio, or six more years at work in the FS, or 1 per cent per annum in terms of the real interest rate. In most developed countries the effect substantially exceeds that of the usually studied biological interest rate.

On the reproductive value and the spectrum of a population projection matrix with implications for dynamic population models.

The eigenvalues of a population projection matrix-except for the Lotka coefficient-are uniquely determined by the reproductive values and the survival. This relation (proposed earlier, but not really well known in western literature) follows from another useful relation between fertility, reproductive values, survival, and Lotka's coefficient. These results are applied to provide demographic interpretations to the intrinsically dynamic and metastable population models by Schoen and co-workers.

On the definition of the reproductive value: response to the discussion by Bacaër and Abdurahman.

The note attempts to address concerns expressed by Bacaër and Abdurahman (J Math Biol, 2008) in this journal about the definition of generalized reproductive value (RV) as proposed by Ediev (Theor Popul Biol 72(4):480-484, 2007).

On an extension of R.A. Fisher's result on the dynamics of the reproductive value.

A classical result by Fisher concerning reproductive value dynamics is extended to the case of varying vital rates with a constant cohort Lotka's r. Based on the demographic potential approach, a generalization of the concept of reproductive value is introduced, which exhibits exponential dynamics both in the classical case of constant vital rates and in a wider class of populations. The generalized reproductive value introduced in this paper fits the classical interpretation by Fisher as a discounted sum of future births in the general class of models addressed here. Our results show when Fisher's classical results may be used as good approximations. They could also be of importance for estimating the fitness of biological populations, aggregate population modeling, and studying the long-term consequences of varying vital rates.